Estimating C4 photosynthesis parameters by fitting intensive A/Ci curves

  • Haoran ZhouEmail author
  • Erol Akçay
  • Brent R. Helliker
Original Article


Measurements of photosynthetic assimilation rate as a function of intercellular CO2 (A/Ci curves) are widely used to estimate photosynthetic parameters for C3 species, yet few parameters have been reported for C4 plants, because of a lack of estimation methods. Here, we extend the framework of widely used estimation methods for C3 plants to build estimation tools by exclusively fitting intensive A/Ci curves (6–8 more sampling points) for C4 using three versions of photosynthesis models with different assumptions about carbonic anhydrase processes and ATP distribution. We use simulation analysis, out of sample tests, existing in vitro measurements and chlorophyll-fluorescence measurements to validate the new estimation methods. Of the five/six photosynthetic parameters obtained, sensitivity analyses show that maximal-Rubisco-carboxylation-rate, electron-transport-rate, maximal-PEP-carboxylation-rate, and carbonic-anhydrase were robust to variation in the input parameters, while day respiration and mesophyll conductance varied. Our method provides a way to estimate carbonic anhydrase activity, a new parameter, from A/Ci curves, yet also shows that models that do not explicitly consider carbonic anhydrase yield approximate results. The two photosynthesis models, differing in whether ATP could freely transport between RuBP and PEP regeneration processes yielded consistent results under high light, but they may diverge under low light intensities. Modeling results show selection for Rubisco of low specificity and high catalytic rate, low leakage of bundle sheath, and high PEPC affinity, which may further increase C4 efficiency.


A/Ci curves C4 Estimation method Non-linear curve fitting Photosynthesis parameters Vcmax Electron transport PEP carboxylation rate Carbonic anhydrase 



Light absorptance of leaf


Rubisco carboxylation assimilation rate


RuBP carboxylation and PEPc carboxylation limitation assimilation


RuBP regeneration and PEP carboxylation limitation assimilation


Gross CO2 assimilation rate per unit leaf area


RuBP regeneration assimilation rate


Net CO2 assimilation rate per unit leaf area


RuBP carboxylation and PEPc regeneration limitation assimilation


RuBP regeneration and PEPc regeneration limitation assimilation


The fraction of O2 evolution occurring in the bundle sheath


Scaling constant for temperature dependence for parameters


Lower boundary CO2 under which assimilation is limited by RuBP carboxylation and PEPc carboxylation


Higher boundary CO2 above which assimilation is limited by RuBP regeneration and PEPc regeneration


Bundle sheath CO2 concentration


Intercellular CO2 concentration


Mesophyll CO2 concentration


Energy of activation for temperature dependence for parameters


Energy of deactivation for temperature dependence for parameters


Entropy for temperature dependence for parameters

\(\phi_{{_{\text{PSII}} }}\)

Quantum yield


The specificity of Rubisco at 25 °C


Bundle sheath conductance for CO2


Bundle sheath conductance for O2


Mesophyll conductance for CO2


Light intensity


Maximum rate of electron transport at 25 °C at a specific light intensity


Maximum rate of electron transport at 25 °C


Michaelis–Menten constant of Rubisco activity for CO2 at 25 °C


Michaelis–Menten constants of Rubisco activity for O2


Michaelis–Menten constants of PEP carboxylation for CO2


O2 concentration in the bundle sheath cells

Q10 for Kp

Temperature sensitivity parameter for Kp


The molar gas constant


Daytime respiration


Daytime respiration in bundle sheath cells


Daytime respiration in mesophyll cells


Ribulose-1,5-bisphosphate carboxylase/oxygenase




Leaf absolute temperature


Velocity of Rubisco carboxylation


Maximal velocity of Rubisco carboxylation at 25 °C


PEP carboxylation


PEPc reaction rate


Maximal PEP carboxylation rate at 25 °C


PEP regeneration rate


The maximal ratio of total electron transport could be used for PEP carboxylation



We are grateful for support from the University of Pennsylvania. We thank Dr. Jesse Nippert, Kansas State University, for providing the fluorometer chamber.


We sincerely thank the constructive comments from two anonymous reviewers. The experiments are supported by Department Research Fund (to H.Z.) from Department of Biology, University of Pennsylvania.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

11120_2019_619_MOESM1_ESM.xlsx (57 kb)
Supplementary material 1 (XLSX 56 KB) Supplementary Material I. Deriving C4 photosynthesis parameters by fitting A/Ci curves for model without carbonic anhydrase reaction using Sharkey’s fitting procedure.
11120_2019_619_MOESM2_ESM.xlsx (68 kb)
Supplementary material 2 (XLSX 67 KB) Supplementary Material II. Deriving C4 photosynthesis parameters by fitting A/Ci curves for model without carbonic anhydrase reaction using Yin’s fitting procedure.
11120_2019_619_MOESM3_ESM.xlsx (59 kb)
Supplementary material 3 (XLSX 59 KB) Supplementary Material III. Deriving C4 photosynthesis parameters by fitting A/Ci curves for model with carbonic anhydrase reaction using Sharkey’s fitting procedure.
11120_2019_619_MOESM4_ESM.docx (26.1 mb)
Supplementary material 4 (DOCX 26768 KB) Supplementary Material IV. Estimation results for two estimation methods of with/without carbonic anhydrase reaction for nine species (using Supplementary Material I and III).
11120_2019_619_MOESM5_ESM.xlsx (35 kb)
Supplementary material 5 (XLSX 34 KB) Supplementary Material V. Instruction for use and set the solver macro.
11120_2019_619_MOESM6_ESM.xlsx (49 kb)
Supplementary material 6 (XLSX 49 KB) Supplementary Material VI. Resources and data for Temperature dependence of input and output parameters.
11120_2019_619_MOESM7_ESM.docx (156 kb)
Supplementary material 7 (DOCX 156 KB) Supplementary Methods, Tables and Figures.
11120_2019_619_MOESM8_ESM.r (11 kb)
Supplementary material 8 (R 10 KB) C4Estimation 0.1.tar.gz is the R package which contains estimation methods for model with and without carbonic anhydrase reaction using Sharkey and Yin’s fitting procedures (same with Supplementary Material I, II and III) and three additional methods in which researchers can provide new temperature response parameters further.
11120_2019_619_MOESM9_ESM.rd (3 kb)
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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of BiologyUniversity of PennsylvaniaPhiladelphiaUSA

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